OK. We've eliminated the 'cheap and easy' possible causes (although gawd knows what a new fan would cost
) so that leaves the much more possible clogged radiator.
Your choice as to whether you strip and see how bad it is or take it to the stealers. They will not do anything to the rad if it isn't too bad to resurrect, they will simply fit a new rad. Let's face it, a couple of snotty tissues chucked out of a car could be all that is making it overheat and papier mache is easy to remove.
When you say 'take it to a BMW specialist' I assume you mean a BMW franchised main dealer. If it needs a new rad you will get a 2 year warranty on the rad and their work will be guranteed in the event of any problems.
PS If the bike is a commuter, the only one you have and is vital for getting you to work, with summer coming it might be better to bite the bullet. As Rae says though, you can always improve the condition of the rad if it isnt' concreted.